1. Technical Field
The present disclosure relates to a control device for resonant converters.
2. Description of the Related Art
Forced switching converters (switching converters) with devices used for controlling them are known in the state of the art. Resonant converters are a wide range of forced switching converters characterized by the presence of a resonant circuit playing an active part in determining the input-output power flow. In these converters, a bridge (half-bridge) consisting of four (two) power switches (typically MOSFET power transistors), which is supplied by a direct voltage, generates a voltage square wave that is applied to a resonant circuit tuned to a frequency close to the fundamental frequency of the square wave. Thereby, because of its selective features, the resonant circuit mainly responds to this fundamental component while negligibly to the higher-order harmonics of the square wave. As a result, the circulating power may be modulated by changing the frequency of the square wave, holding the duty cycle constant at 50% and, according to the resonant circuit configuration, the currents or voltages associated with the power flow have a sinusoidal or a piecewise sinusoidal shape.
These voltages are rectified and filtered so as to provide d.c. power on the load. In offline applications, for security requirement issues, the rectification and filtering system supplying the load is coupled to the resonant circuit by a transformer providing the isolation between source and load required by the above-mentioned regulations. As for all the isolated network converters, also in this case a distinction is made between a primary side (as related to the primary winding of the transformer) connected to the input source and a secondary side (as related to the secondary winding—or to the secondary windings—of the transformer) providing power to the load through the rectification and filtering system.
Among the many types of resonant converters, the so-called LLC resonant converter, especially in the half-bridge version thereof, is widely used. Such a designation comes from the fact that the resonant circuit employs two inductors (L) and a capacitor (C); a principle schematic of an LLC resonant converter is shown in FIG. 1. Resonant converter 1 has a half-bridge of transistors Q1 and Q2 between the input voltage Vin and the ground GND and driven by a driving circuit 3. The common terminal HB between the transistors Q1 and Q2 is connected to a circuit block 2 that has a series of a capacitor Cr, an inductance Ls, and another inductance Lp connected in parallel to a transformer 10 with a center-tap secondary. The two windings of the center-tap secondary of the transformer 10 are connected to the anodes of two diodes D1 and D2, whose cathodes are both connected to the parallel of a capacitor Cout and a resistance Rout; across the parallel Rout, Cout there is the output voltage Vout of the resonant converter, while the output current Iout flows through the resistance Rout.
The resonant converters offer considerable advantages as compared to the traditional switching converters (non-resonant, typically PWM—Pulse Width Modulation—controlled): wave forms without steep edges, low switching losses of the power switches due to the “soft” switching thereof, high conversion efficiency (>95% is easily reachable), ability to operate at high frequencies, low EMI (Electro Magnetic Interference) generation and, ultimately, high power density (enabling to achieve conversion systems capable of handling considerable powers in relatively small space).
As in most dc-dc converters, a closed-loop, negative feedback control system keeps the output voltage of the converter constant upon changing the operating conditions, that is the input voltage Vin or the output current Iout thereof. This is achieved by comparing a portion of the output voltage with a reference voltage Vref. The difference or error signal Er between the value provided by the output voltage sensing system (usually, a resistance divider) and the reference value is amplified by an error amplifier whose output Vc modifies a quantity x inside the converter which the energy carried by the converter in each switching cycle substantially depends on. As set forth above, such a significant quantity in resonant converters is the switching frequency of the square wave stimulating the resonant circuit.
Again, as is common in the control systems of the dc-dc converters, the frequency response of the error amplifier must be properly designed so as to ensure:                a stable control loop (i.e., the fact that upon disturbances of the operating conditions of the converter, once the transient caused by the disturbance is finished, the output voltage tends to recover a constant value close to the value before the perturbation;        a good regulation (i.e., the new constant value recovered by the output voltage following a disturbance is very close to that before the disturbance);        good dynamic performance (i.e., during the transient following a disturbance the output voltage is not so different from the desired value and the transient itself is short).        
The above-mentioned control objectives may be expressed in terms of some characteristic quantities of the transfer function of the control loop, such as the bandwidth, the phase margin, and the d.c. gain. In a dc-dc converter, these objectives may be achieved by acting on the frequency response of the error amplifier, by modifying the gain thereof and conveniently placing the poles and zeroes of its transfer function (frequency compensation), which is normally achieved by using passive networks having resistances and capacities of appropriate value connected thereto.
In order to determine which is the required frequency compensation to obtain the desired features of the transfer function of the control loop, however, it must be known in advance both the gain of the modulator, i.e., the system converting the control voltage Vc into the control quantity x, as well as the frequency response of the converter itself to the variations of quantity x.
The modulator gain does not usually depend on the frequency, at least within the range of the relevant frequencies, which may not be higher than half of the switching frequency of the converter by virtue the Shannon's theorem, and it is fixed within the control integrated circuit.
As far as the frequency response of a dc-dc converter, even in the presence of a strongly non-linear system just because of the switching action, with suitable approximations and under certain hypothesis, this may be described and represented by the same means used for the linear networks and, therefore, by a transfer function characterized by gain, zeroes and poles. This transfer function essentially depends on the topology of the converter, i.e., on the mutual configuration of the elements handling the power, the operation mode thereof, i.e., whether, at every switching cycle, there is a continuous current circulation in the magnetic part (Continuous Current Mode, CCM) or not (Discontinuous Current Mode, DCM), the quantity x which is controlled by the control loop. While in PWM converters different control methods are commonly used—e.g., the width of the pulse controlling the power switches (direct duty cycle control and, therefore, x=D) or the peak of the current flowing through the switches (peak current mode control, x=Ip) are directly acted upon—traditionally, in resonant converters, the quantity used to control the converter is directly the switching frequency of the square wave applied to the resonant circuit.
In all the integrated control circuits for dc-dc resonant converters available in the market, the control directly operates on the oscillation frequency of the half-bridge (Direct Frequency Converter, DFC). FIG. 2 shows a control system for this type of resonant converters. The output of the error amplifier 4, having a part of the output voltage Vout at the input of the inverting terminal and a reference voltage Vref at the non-inverting terminal, on the secondary side is transferred to the primary side by a photo-coupler 5 so as to ensure the primary-secondary isolation according to the security requirements and acts upon a voltage-controlled oscillator (VCO) 6 or a current-controlled oscillator (ICO) inside the control integrated circuit 30.
This type of control arises two classes of problems. A first class relates to the fact that the dynamic small-signal models for resonant converters expressed in terms of gain, poles and zeroes are not known in literature (but in some approximated forms of questionable practical use), differently from what occurs, instead, for PWM converters, i.e., the transfer function of the power stage is not known. A second class of problems relates to that, according to study results based on simulations, the transfer function of the power stage shows a strongly variable d.c. gain, and a variable number of poles from one to three and with very mobile position, depending on the operating point. Finally, there is a zero due to the output capacitor.
The considerable variation of the gain and the so-highly variable pole configuration make the frequency compensation of the feedback control loop quite problematic. As a result, it is virtually impossible to obtain a transient response optimized under all the operating conditions, and a considerable trade-off between stability and dynamic performances is required. Furthermore, there is a strong dependence of the energy transfer on the input voltage (audio susceptibility), whereby the control loop must strongly intervene and considerably change the operating frequency for compensating the variations. Taking into account that an alternate component with a frequency twice that of the main voltage always exists in the input voltage of the converter, the loop gain at that frequency needs to be quite high, so as to effectively reject the alternate component and considerably attenuate the residual ripple visible in the output voltage.
All these factors present problems not completely solvable, particularly when the load supplied by the converter has considerable dynamic changes and/or the specifications on the dynamic accuracy or the response speed or the rejection of the input ripple is strict.
Finally, another problem related to the DFC control method is that of the statistical spread of values of the components of the resonant circuit (Cr, Ls and Lp) due to their tolerances. Indeed, generally speaking, in order to avoid a converter from abnormally operating, the control quantity x should be limited. In this case, the resonant controllers implementing DFC allow the operational frequency of the half-bridge to be high- and low-limited. These limits should be set by taking into account that, due to the above-mentioned value spread, the operating frequency range of the converter will change accordingly. Therefore, the minimum limit set to the frequency should be lower than the minimum value which could be taken by the lower end of the range, and the maximum limit should be higher than the maximum value which could be taken by the higher end of the range. This considerably reduces the effectiveness of the frequency limitation as a means for preventing abnormal operating conditions.
One approach reported in the literature is that described in the article “Self-Sustained Oscillating Resonant Converters Operating Above the Resonant Frequency” to H. Pinheiro, P. K. Jain, and G. Joos, published in IEEE Transactions on Power Electronics, Vol. 14, No. 5, September 1999, p. 803-814, wherein the quantity x which is controlled by the feedback loop is the phase shifting between the current of the resonant circuit and the square wave voltage applied to the circuit by the half-bridge or bridge. In the above-mentioned article it is shown that, since said phase shifting has values within a fixed range (from 0 to 90° late) regardless of the features of this resonant circuit and the operating conditions, the control variable will also have the same independence property. In the “control terminology” this is called a “robust control.” Again, it is shown that the system obtained is absolutely stable in any operational conditions, provided that the current of the resonant circuit is late with respect to the voltage applied thereto. This restraint coincides with the necessary condition to obtain the “soft” switching for the MOSFET transistors belonging to the half-bridge.